String quartets: Mozart vs. Haydn

Markov chain models are built up for Mozart's and Haydn's scale degree class transitions. The repertoire consists of all of their string quartets, 100 movements from Mozart and 212 movements from Haydn. The scale degree is defined relative to the tonics, i.e., all works are transposed into the same key. Also, for the sake of reducing the dimensionality of transition matrice, the system does not distinguish between the same degree class at different octaves. The system does not distinguish between major keys and minor keys, either. Then, the two-way identification tests based on Kullback-Leibler distances were conducted for each of the 4 voices. The tests were conducted in a bootstrap manner. In other words, it is always assumed that the computer has been exposed to the all the works in the repertoire except the one to be identified.

Table 1: Mozart vs. Haydn identification tests.

Part	Mozart	Haydn
ViolinI	68.0%	64.2%
ViolinII	58.0%	64.2%
Viola	61.0%	53.8%
Cello	57.0%	52.8%

Table 1 shows the result of two-way identification tests. The boldfont indicates data that are statistically significant. To qualify for statistical significance, a recognition rate has to be higher than $\mu + 2\sigma$ of random flips of fair coins, where $\mu$ is the mean, 50%; and $\sigma$ is the standard deviation, which is inversely proportional to the square root of the number of flips, according to the central limit theorem.

As a controlled experiment, repertoires are defined as two randomly assigned, and mutually exclusive lists of quartets. Then, the two-way style identification tests are conducted, and the result is shown in Table 2. Each of the data shows an average of ten runs.

Table 2: Random repertoires identification tests.

Part	Random A	Random B
ViolinI	42.6%	56.1%
ViolinII	44.5%	53.4%
Viola	47.4%	51.9%
Cello	43.1%	53.4%

Human listening tests are conducted via web survey. A user is played, the MIDI piano version of, a quartet from either composer by equal chance, and is asked to identify the composer. As of June 11, 2002, web users average 59.0% of accuracy in 1865 attempts. How experienced the users are with the repertoire ranges from novices of classical music to string players that have played some of the works.